Motivated by recent experiments [Vera-Marun et al., arXiv:1109.5969], we
formulate a non-linear theory of spin transport in quantum coherent conductors.
We show how a mesoscopic constriction with energy-dependent transmission can
convert a spin current injected by a spin accumulation into an electric signal,
relying neither on magnetic nor exchange fields. When the transmission through
the constriction is spin-independent, the spin-charge coupling is non-linear,
with an electric signal that is quadratic in the accumulation. We estimate that
gated mesoscopic constrictions have a sensitivity that allows to detect
accumulations much smaller than a percent of the Fermi energy.Comment: 4 pages, 3 figure